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## Polibits

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*On-line version* ISSN 1870-9044

### Polibits n.51 México Jan./Jun. 2015

#### http://dx.doi.org/10.17562/PB-51-7

**The Multiple Knapsack Problem Approached by a Binary Differential Evolution Algorithm with Adaptive Parameters**

**Leanderson André and Rafael Stubs Parpinelli**

*The authors are with the Graduate Program in Applied Computing, Departament of Computer Science, State University of Santa Catarina, Joinville, Brazil.* (e-mail: leanderson.andre@gmail.com, rafael.parpinelli@udesc.br).

Manuscript received on January 20, 2015,

Accepted for publication on March 8, 2015,

Published on June 15, 2015.

**Abstract**

In this paper the well-known 0-1 Multiple Knapsack Problem (MKP) is approached by an adaptive Binary Differential Evolution (ABDE) algorithm. The MKP is a NP-hard optimization problem and the aim is to maximize the total profit subjected to the total weight in each knapsack that must be less than or equal to a given limit. The ABDE self adjusts two parameters, perturbation and mutation rates, using a linear adaptation procedure that changes their probabilities at each generation. Results were obtained using 11 instances of the problem with different degrees of complexity. The results were compared using aBDE, BDE, a standard Genetic Algorithm (GA) and its adaptive version (AGA), and an island-inspired Genetic Algorithm (IGA) and its adaptive version (AIGA). The results show that ABDE obtained better results than the other algorithms. This indicates that the proposed approach is an interesting and a promising strategy to control the parameters and for optimization of complex problems.

**Key words:** Adaptive parameter control, binary differential evolution, multiple knapsack problem, evolutionary computation.

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